Condensation of bosons causes spectacular phenomena such as superfluidity or superconductivity. Understanding the nature of the condensed particles is crucial for active control of such quantum phases. Fascinating possibilities emerge from condensates of light-matter-coupled excitations, such as exciton-polaritons, photons hybridized with hydrogen-like bound electron-hole pairs. So far, only the photon component has been resolved, while even the mere existence of excitons in the condensed regime has been challenged. Here we trace the matter component of polariton condensates by monitoring intra-excitonic terahertz transitions. We study how a reservoir of optically dark excitons forms and feeds the degenerate state. Unlike atomic gases, the atom-like transition in excitons is dramatically renormalized on macroscopic ground state population. Our results establish fundamental differences between polariton condensation and photon lasing and open possibilities for coherent control of condensates.